Inclusion Criteria:
1. Patient must be \>/=18 years of age at time of signing informed consent;
2. Patient has histologically and/or cytologically confirmed diagnosis of advanced or metastatic selected solid tumors.
3. Patient must have progressed on at least 1 prior line of therapy in the advanced or metastatic setting that is considered an appropriate standard of care. In general, if maintenance therapy is part of the standard of care, it should be considered as part of the "1 prior line of therapy in the advanced or metastatic setting" requirement;
4. Patient must fulfill genomic selection criteria: prior available documented evidence in tissue or blood (circulating tumor DNA \[ctDNA\]) of the genetic alterations indicated below. The Sponsor Medical Monitor or delegate must confirm eligibility based on the reported genomic alteration and applicable assay cut off criteria prior to patient enrollment.
• Patients with BRCA1/2 mutations (germline or somatic, pathogenic or likely pathogenic) and other mutations signifying HR deficiency or high replication stress.
• For Dose Expansion: Tumor types for Dose Expansion cohorts include a subset of tumors specified in Inclusion Criterion 3 as follows: i) Cohort 1: Advanced or metastatic breast cancer independent of hormone receptor status and documented evidence of prior treatment with a locally approved PARP inhibitor(s); ii) Cohort 2: Advanced or metastatic ovarian cancer with prior available documented evidence in tissue or blood (ctDNA) of specific genomic abnormalities.
iii) Cohort 3: Advanced or metastatic breast cancer with prior available documented evidence in tissue or blood (ctDNA) of specific genomic abnormalities.
Note: Diagnostic genetic testing for Dose Escalation/backfilling and Dose Expansion cohorts must meet the following requirements:
• United States (US): Testing must have been performed using a College of American Pathologists/Clinical Laboratory Improvement Amendments (CAP/CLIA)-certified laboratory developed test (LDT) or a Food and Drug Administration (FDA)-approved diagnostic test.
5. Patient has measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 at Clinical Screening; Note: Tumor lesions situated in a previously irradiated or otherwise locally treated area will be considered measurable provided that there has been clear imaging-based progression of the lesion since the time of local treatment.
6. Patient has adequate bone marrow and organ function, defined by the following laboratory results obtained within 14 days before first dose of study drug:
* Platelet count \>/=100 × 10\^9/L (\>/=100,000/μL) (absence of platelet transfusion within 1 week);
* Hemoglobin \>/=90 g/L (\>/=5.6 mmol/L) (absence of red blood cell transfusion within 2 weeks);
* Absolute neutrophil count \>/=1.5 × 10\^9/L (\>/=1500/μL) (absence of growth factors within 2 weeks);
* Aspartate aminotransferase and alanine aminotransferase \</=2.5 × upper limit normal (ULN) or \</=5 × ULN for patients with liver metastases;
* Total bilirubin \</=1.5 × ULN, or \</=3.0 × ULN for patients with liver metastases or Gilbert's syndrome;
* Estimated glomerular filtration rate \>/=60 mL/min calculated by the 2021 Chronic Kidney Disease Epidemiology Collaboration Equation; and
* Adequate coagulation test results defined by activated partial thromboplastin time \</=1.5 × ULN, international normalized ratio (INR) \</=2.0 with the exception of INR 2 to 3 acceptable for patients on warfarin anticoagulation or direct oral anticoagulants.
7. Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 to 2 with \>/=3 months of life expectancy for Dose Escalation cohorts, and an ECOG PS of 0 to 1 with \>/=3 months of life expectancy for backfilling and Dose Expansion cohorts;
8. Patient is able to swallow tablets and has no gastrointestinal conditions affecting absorption.
Exclusion Criteria:
1. Patient has received anti-cancer treatment or an investigational agent \</=14 days or 5 half-lives prior to first dose, whichever is shorter, or patient has received immunotherapy \</=28 days prior to first dose; Note: Localized radiotherapy given with palliative intent is allowed and should be completed 1 week or more before receiving the first dose of FORX-428. It may also be allowed after the dose-limiting toxicity (DLT) Observation Period, pending discussion with the Sponsor Medical Monitor or delegate and their approval.
2. Patient has had previous exposure to a PARG inhibitor;
3. Patient has a history of other malignancy diagnosed \</=5 years prior to consent, except for any locally occurring cancer that has been treated with curative intent with no evidence of disease for \>2 years at the time of consent and includes the following: completely resected cervical carcinoma in situ, basal or squamous cell skin cancer, ductal carcinoma in situ, superficial bladder cancer, or early-stage prostate cancer which has been adequately treated;
4. Patient has had major surgery within 30 days prior to first dose of study drug (with exceptions further defined in the protocol), or anticipation of major surgery during study treatment;
5. Patient has impaired cardiovascular function or clinically significant cardiovascular disease as further stipulated in the protocol;
6. Patient has uncontrolled HIV or hepatitis C infection;
7. Patient has known metastatic central nervous system malignant disease or leptomeningeal disease; Note: Patients previously treated for brain metastasis who are asymptomatic, receiving \</=10 mg/day prednisone equivalent, not requiring anti-epileptic therapy, and without evidence of radiological progression for at least 4 weeks are allowed.
